When Doc shoots the man in his office there is no bullet hole in the sheet behind him.
As a kid Charles had a scar on the left side of his cheek but as he is older there should have been a scar there.
In the first scene the man uses plastic shotgun shells.
After they blow the zombie's head off, they pull out a flame thrower and burn the body. Flame throwers of that type weren't in use until the 20th century.